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The Validity of Multinomial Logistic Regression and Artificial
Neural Network in Predicting Sukuk Rating: Evidence from Indonesian
Stock Exchange

Muhammad Luqman Nurhakim

Zainul Kisman*

Faizah Syihab

Published 2 November 2020

The Sukuk (shariah bond) market is developing in Indonesia and potentially will capture the global market in the future. It is an attractive investment product and a hot current issue in the capital market. Especially, the problem of predicting an accurate and trustworthy rating. As the Sukuk market developed, the issue of Sukuk rating emerged. As ordinary investors will have difficulty predicting their ratings going forward, this research will provide solutions to the problems above. The objective of this study is to determine the Indonesian Sukuk rating determi- nants and comparing the Sukuk rating predictive model. This research uses Arti- ficial Neural Network (ANN) and Multinomial Logistic Regression (MLR) as the predictive analysis model. Data in this study are collected by purposive sampling and employing Sukuk rated by PEFINDO, an Indonesian rating agency. Findings in this study are debt, profitability and firm size significantly affecting Sukuk

*Corresponding author.

Review of Pacific Basin Financial Markets and Policies Vol. 23, No. 4 (2020) 2050032 (24 pages) °c World Scientific Publishing Co.

and Center for Pacific Basin Business, Economics and Finance Research DOI: 10.1142/S0219091520500320

rating category and the ANN performs better predictive accuracy than MLR. The implications of the results of the research for the issuer and bondholder are a higher level of credit enhancement, a higher level of profitability, and the bigger size of firm rewarding higher Sukuk rating.

Keywords: Sukuk rating; forecasting models; artificial neural network; multinomial logistic regression.

JEL Classifications: G1, C45, C52, C53

1. Introduction

August 2018, the accumulative amount of corporate Sukuk issuance raised

from IDR 26,394.90 billion to IDR 30,933.40 billion. Growth during the six-

month period recorded at 17.19%, Indonesia’s Authority of Financial Service

(OJK) stated in its report. Standing Committee for Economic and Com-

mercial Cooperation of the Organization of Islamic Cooperation (COMCEC)

stated in its report on Sukuk market development in 2018 that the Indo-

nesian Sukuk market is currently considered as developing market and yet it

has a significant potential to capture global Sukuk market share in the future

(COMCEC, 2018). Sukuk itself is popularly known as shariah bond, though

in fact, both Sukuk and bond is basically and fundamentally different.

COMCEC research report explained that Sukuk is not an interest-bearing

financial as the way bond is but it possesses a similar function as a financial

instrument in the money market (COMCEC, 2018).

According to Giap et al. (2018), in spite of the positive development

execution of Indonesia in the course of recent decades, concerns have been

communicated about whether the nation would be trapped in a middle-

income trap. So, this study believes industry financing using Sukuk is a

solution so that the country can get out of a middle-income trap.

Moreover, according to Khartabiel et al. (2019), companies do not have to

worry about issuing Sukuk because, in the postcrisis period (2008), the

market reaction for Sukuk is positive and significant, apparently due to new

market participants’ views, awareness and increased demand for Islamic

financial products, whereas the conventional bonds do not have a significant

market reaction. This is why discussions about Sukuk are important, espe-

cially for Indonesia and other developing countries about how to accurately

predict ratings.

Kartiwi et al. (2018) stated the development of Sukuk emerged issues on

Sukuk rating that shows the issuer’s creditworthiness. Indonesia’s Rating

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Agency (PEFINDO) explained in its release that credit rating is indicating

the issuer’s capacity to fulfill long-term financial commitment under shariah

principles contract. This issue on Sukuk rating is not only about what Sukuk

rating one issuer is but also factors that determine the issuer’s rating. The

later mentioned issue is highly discussed in Sukuk field research mostly in

the mature Sukuk market country, Malaysia. The main problem in rating

issue is rating agency cannot be widely transparent on what factor people

need to know unless the final result, rating. Rating agencies limited access to

detailed rating methodology and people found this to be too complicated to

understand and according to DeBoskey and Gillett (2011) felt the lack of

corporate transparency. Then, Chu et al. (2019) noted the results of his

research that increased transparency of information can reinforce invest-

ment certainty and lead to fewer forecast errors.

This research’s objective is to give a better approach toward Sukuk rating

understanding for the common investor. A better approach can be provided

by using the most popular factors that can be easily recognized. Factors

involved will be tested for its significance to build a predictive model of

Sukuk rating. The predictive model will be tested in both multinomial lo-

gistic regression and artificial neural network than comparing their predic-

tive accuracy. Findings in this study hopefully can provide a better and

simplified approach for Indonesian Sukuk investors.

2. Theoretical Framework

2.1. Sukuk

Sukuk’s origin from the Arabic word \sack" literally means cheque or cer-

tificate. As for Borhan and Ahmad (2018), Sukuk is all form of intention as a

contract symbol or transferring rights, debt, or money. Ahmed et al. (2014)

stated that Sukuk is a certificate of equal value that represents an undivided

share on ownership of tangible assets, services, a certain project, or in-

vestment. As stated before, Sukuk is popularly known as shariah bond.

COMCEC reported that Sukuk is a financial instrument in the market as an

answer to the needs of shariah compliance instruments that work similarly to

a bond (COMCEC, 2018). Shariah compliance instruments must obey

shariah principles to avoid riba, gharar, maysir, injustice, and the activity of

investment must be permitted by shariah (Dusuki, 2012).

There are differences between Sukuk and bond. Mseddi and Naifar (2013)

stated Table 1 that bond is a pure debt contract between investor and issuer

that issuer uses to finance all kinds of business activity and valued based on

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the issuer’s credit worthiness. While, Sukuk is a certificate of trust that

represent ownership interest, specific assets, specific services, or project that

certified by the third party. Sukuk equaling bond’s function as it gives return

and paid at due. The differences that separate Sukuk and bond fundamen-

tally are the underlying for the contract, the relationship between investors

and issuers, and sale price. Bond is based on the loan, while Sukuk must not

be based on the loan. Sukuk’s underlying must comply with Shariah prin-

ciples and depends on the type of Sukuk issued. The relationship in the bond

is definitely debts relationship, borrowers and lenders. Relationship in Sukuk

will depend on its underlying and type of contract, in Mudharabah Sukuk

the relationship is a partnership. Then the bond can be sold on premium or

discount, while Sukuk must be sold at its fair value.

There are so many Sukuk classifications, yet some literature used the

asset-based and asset-backed classification. The Securities Commission

Malaysia report stated that this classification is due to its technical and

commercial features. The difference between these two types of Sukuk is

mainly on how underlying assets treated as Sukuk must have underlying

assets. Asset-based Sukuk is occurring when there is no true sale of assets to

Table 1. Sukuk and bond.

Differences Sukuk Bond

Ownership Clearly regulated Holder rightful of cash flow from pure debt

The contract between issuer and holder

Based on financing or certain business

Purely getting money from money

Underlying asset nature and usage

Shariah compliance As long as not against the jurisdiction

Operation of sale Sale of assets, investment, or project

Sale of debt

Expense on assets Probably stick to Sukuk holders None Securitization Price Based on its underlying assets

fair value Depends on issuer’s credit

worthiness Risk and return Explicit share on risk and return

based on profit generated by underlying assets

Holders endure low risk and return based on the coupon

Instrument trading Depend on underlying assets nature

No prohibition

No prohibition

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investors, which means that the assets remain in the issuer’s balance sheet.

Whilst-backed Sukuk is occurring when there is true sale. The ownership of

assets is legally transferred into investors. Literatures stated that the main

different between these two types of Sukuk is significant when default occurs

in Herzi (2016) and Rachmawati and Ghani (2015). Asset-backed is pref-

erable at default, this type is more secure than asset-based in these cir-

cumstances. Asset-based investors can sell the assets when default. On the

other hand, asset-based ultimate recourse at default is the buyback clause.

Therefore, asset-based highly considers the issuer’s creditworthiness.

Indonesian corporate Sukuk does not vary in the market, though there are

so many types of contracts in Sukuk issuance. COMCEC report stated that

based on the National Shariah Board (DSN) data on Sukuk issuance in 2016,

corporate mainly issued ijarah and mudharabah type of Sukuk (COMCEC,

2018). Indonesian Directorate of Shariah Finance defined Sukuk ijarah as a

type of Sukuk that based on the ijarah contract. The underlying of Sukuk

ijarah is the asset that its beneficial ownership is sold to investors. The

underlying assets will remain in obligor’s possession and obligor obliged to

pay the investor the rent for the use of underlying assets. Obligor then buys

this underlying asset back at its fair value as due. Indonesian Directorate of

Shariah Finance stated that Sukuk mudharabah is the type of Sukuk based

on the mudharabah contract. The relationship between investors and issuer

is a partnership where investor as the capital provider and as the one that

works on the investment project. Sukuk mudharabah will divide profit

gained from the investment project based on the agreement and loss will be

entirely investors exposure.

2.2. Sukuk rating

Sukuk rating, aforementioned, is indicating the issuer’s capacity to fulfill its

long-term financial commitment under shariah contract. PEFINDO rating

agency revealed its rating process in its release on securitization that found

to be complicated to understand. The release stated the type of analysis in

rating Sukuk. In short, the rating methodology analyzes risk, credit en-

hancement, assets, assets management, and cash flows to classify the issuer’s

rating. Though the analysis process was briefly described, it remains unclear

what should be concerned in rating issues. The rating analysis is as follows:

(1) An industry analysis conducted to investigate the characteristics and

risk profile of an industry that relates to assets in many aspects.

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(2) Determine \Benchmark Pool", industry analysis result used to deter-

mine the benchmark pool that PEFINDO uses to measure risk factors of

assets.

(3) Determine \Base Default Frequency (BDF)", purposed to measure ex-

pectancy level on loss and credit enhancement for each rating category.

The higher the rating, securitization needs higher credit enhancement.

Nonperforming Loan (NPL) is a factor to determine the BDF value.

(4) Servicer Evaluation, stage of evaluating the capability of the servicer in

managing securitized assets.

using benchmark pool and BDF.

(6) Securitization structure analysis assessing the risk profile of securitiza-

tion transaction structure by evaluating security scheme, security

agreement analysis, protection on credit risk, legal aspect, and audit

result analysis.

(7) Cash flow analysis, measuring cash flow adequacy generated by securi-

tized assets compare to expenses.

2.3. 5C of credit

Sukuk rating indicates the issuer’s capacity that relates to the issuer’s cred-

itworthiness. Creditworthiness is also found important in Sukuk, whereas

asset-based Sukuk holder relies only on obligor’s creditworthiness since

the underlying assets remain on obligor’s balance sheet. Peprah et al.

(2017) explained that creditworthiness assessed by 5C principles of credit, as

follows:

analysis mainly investigates borrowers’ good will to repay debt.

(2) Capital, very important analysis to measure borrower’s capability to

endure market and unexpected risk.

(3) Capacity, Sharma and Kalra (2015) capacity is an assessment of bor-

rower’s capability to repay debt.

(4) Collateral, purposed to secure financial exposure in case of default.

(5) Condition, analysis of debt purposes, industry, economy, and political

environment.

3. Literature Review

Studies on Sukuk have been growing in numbers since the development of

the Sukuk market around the globe, though quite a few Sukuk rating

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studies. Most studies on Sukuk rating employed in Bursa Malaysia as its

Sukuk market considered at a mature stage, as per the COMCEC report.

Variables in Sukuk rating studies vary but commonly most studies used

financial ratio, macroeconomic factors, and Sukuk itself (COMCEC,

2018). Methodology on Sukuk rating studies also varies though most of the

studies used predictive analysis such as multinomial logistic regression and

ordered logistic regression.

Arundina and Omar (2009) and Borhan and Ahmad (2018) tried to

examine the Sukuk rating determinant in Bursa Malaysia. Analysis of this

study is based on multinomial logistic regression findings and resulted in

the significance of profitability and guarantee status. The influence of

significant factors is all positive toward the Sukuk rating. Firm size is not

a significant factor, though Borhan and Ahmad (2018) stated that firm

size is the prime factor in the Sukuk rating study. Smaoui and Khawaja

(2018) investigated Sukuk’s market development determinant. Interest

spread, the difference between borrowing and lending rate, found to be

negatively influencing Sukuk market development. Elhaj et al. (2015)

found in their study that board size, financial leverage, profitability, firm

size, and Sukuk structure influenced Sukuk’s rating. Elhaj et al. (2015)

found the negative influence of financial leverage represented by debt to

total assets ratio (DAR). Arundina et al. (2015) compared neural network

inferences and multinomial logistic regression in predictive accuracy re-

search on Malaysian Sukuk rating. This study claimed that neural net-

works better logit predictive accuracy. This study also found return on

assets (ROA) and DAR significant. Naifar and Mseddi (2013) showed in

their study that Sukuk yield reacts positively toward stock return index.

4. Methodology

4.1. Data and sample

Data in this study are secondary data taken from various related sources.

Sukuk rated by PEFINDO will be this study’s sample and a sample must

contain all variables value. Sources in this study are PEFINDO releases on

rating, firm’s financial statement, Indonesian stock exchange (IDX), and

Indonesia’s Central Bureau of Statistics (BPS). There are 125 samples col-

lected and filtered by these criteria and issued outlier data and extreme

values used become 63 samples.

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(MLR) used to predict categorical placement or probability of categorical

membership on a dependent variable based on a few independent variables.

MLR is a simple development of binary logistic regression that allows more

than 2 categories dependent variable. MLR equation is as follows:

log pðgroupjÞ pðgroupiÞ ¼ m þ i1X1 þ i2X2 þ i3X3 þ þ inXn :

MLR uses maximum likelihood estimation that maximizes the probability of

dependent variable occurrence by finding a regression coefficient. MLR

assumes the dependent variable category should be independent, multi-

collinearity test, no extreme values or outlier, and nonperfect separation.

There will be two general tests inMLR, the goodness of fit test and significance

test. The goodness-of-fit test provided with three indicators which are2 log-

likelihood test, chi-square test, and pseudoR2.2 log-likelihood will compare

the final model consists of all independent variables against the intercept and

only model. The chi-square test indicates the deviation of predictive proba-

bility against its observed value. Pseudo R2 is said to be R2 and yet it is not

realR2 instead PseudoR2 is the measurement of linear convergence between

the predictive probability and the observation probability. The significance

test will be the partial test and the Wald test. The partial test is indicating

the influence of one independent variable toward the dependent variable.

Wald test will describe the relationship between the independent variable

and the dependent variable’s category. This study will do the predictive test

which will measure MLR model predictive accuracy.

4.3. Arti¯cial neural network

Sena (2017) explains that Artificial Neural Network (ANN) is a nonpara-

metric predictive analysis which imitates the work of human brains. ANN is

part of machine learning, artificial intelligence, and also known as a multi-

layer perceptron. According to Kumar and Haynes (2003), ANN is suc-

cessfully used in financial fields, such as stock price prediction, portfolio

management and selection, and credit rating analysis. Matlab provides types

of ANN that produce different output and ANN Pattern Recognition is

launched to conduct the predictive analysis. ANN Pattern Recognition’s

output is categorical that complies with the study objective to predict the

rating of Sukuk. ANN in Matlab has three stages of test: training, validation,

and test. In the training stage, ANN learned and change weight and bias in

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the network. In the Validation stage, ANN will be generalized to its opti-

mum level that there will be no better performance possible to achieve. In

the test stage, the model will be tested with no effect that increases ANN

performance. Most of the studies using ANN and Matlab indicate that the

prime performance indicator extracted from the validation stage. Two main

indicators are cross-entropy or error degree and confusion matrix that show

predictive accuracy. This study will compare ANN predictive accuracy and

MLR predictive accuracy.

5. Hypothesis

This study tries to find determinants of Sukuk rating by plotting financial

ratios and macroeconomic factors. Independent variables will be elaborate as

follows.

5.1. DAR X1

According to Erica (2018), Gibson (2013) and Gitman and Zutter (2015)

that debt to total assets ratio is the measurement of risk but also a financial

leverage ratio that shows a potential profit in the future. Elhaj et al. (2015),

Arundina et al. (2015) and Pebruary (2016) found DAR significantly af-

fecting Sukuk rating in a negative way. DAR not only represents financial

leverage ratio but also capital in 5C, therefore authors believe that DAR will

significantly affect Sukuk rating.

5.2. ROA X2

Erica (2018), Gibson (2013) and Gitman and Zutter (2015) define that re-

turn on assets represents profitability that shows the capability to generate

profit by the firm’s total assets. Borhan and Ahmad (2018), Elhaj et al.

(2015), Arundina et al. (2015) revealed a positive significant influence of

ROA toward Sukuk rating. Borhan and Ahmad (2018) stated that higher

profitability rewarded by higher Sukuk rating. ROA is also representing

capacity in 5C that ensure issuers to pay their liabilities.

H2: ROA significantly affecting Sukuk’s rating.

5.3. Firm size X3

Firm size is generally measured by total assets in natural logarithm form.

Borhan and Ahmad (2018) stated that there is no significant influence of firm

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size, despite firm size being considered as prime factors in Sukuk rating

studies. While Elhaj et al. (2015) found positive influence by firm size toward

Sukuk rating. Firm size can represent character, capital, and collateral of

5C. The character can be represented as firm size measured by total assets

that show the value of the firm, the higher value means bigger firm and such

big firm will behave as expectedly as explained by Setiadharma and Machali

(2017). This reason is also why it can represent capital that shows the ca-

pability of risk-bearing and collateral as the big firm has more alternatives to

pay liabilities.

5.4. Bank Indonesia (BI) rate X4

BI rate in this study is BI 7 day repo rate that Bank of Indonesia defined as

monetary policy effectively and quickly affects the money market. Smaoui

and Khawaja (2018) found interest spread negatively affect Sukuk market

development. BI rate is considered a macroeconomic factor and represents

the condition of 5C that will significantly affect the Sukuk rating.

H4: BI rate significantly affecting Sukuk rating.

5.5. JII X5

JII stands for Jakarta Islamic Index, JII listed 30 most liquid shariah stock in

the market. Sclip et al. (2016) found a high volatility relationship between

the international stock index and the Sukuk market in the financial crisis.

Naifar and Mseddi (2013) stated that Sukuk yield reacted positively against

the stock return index in Malaysia. As well as BI rate, JII is also considered

as a macroeconomic factor that represents the condition of 5C and will

significantly affect Sukuk rating.

5.6. Predictive accuracy

Arundina et al. (2015) found that Neural Network Inferences better MLR

performances in Malaysian Sukuk rating predictive analysis. Kumar and

Haynes (2003) found that ANN is better that discriminant analysis in pre-

dicting bond rating. ANN is considered a more complex model than MLR

and can suit the complexity level of models.

H6: ANN predictive accuracy higher than MLR predictive accuracy.

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6.1. Introduction

The objective of this study is to find the determinants of Indonesian Sukuk

rating and to decide which method has better predictive accuracy. First, the

authors construct the predictive model which only included the significant

independent variables as described by Widarjono (2015). All independent

variables are continuous variables. While the dependent variable is cate-

gorical. The authors divide the Sukuk rating into three categories: 1, 2, and

3. Category 1 is for BBB and below Sukuk rating, Category 2 is for A Sukuk

rating, and Category 3 is for AA and AAA Sukuk rating. Model predictive

will be selected by launching a stepwise MLR test that enters only the

significant variables and excluded nonsignificant variables. This is due to the

inability of ANN to figure the effective variables to affect the dependent

variables. In order to do so, authors, as aforementioned, conduct stepwise

MLR as a more reliable procedure to construct a predictive model.

6.2. MLR assumption test

The assumption test is necessary to build a good and reliable MLR model.

Therefore, outliers and extreme values in the model must be eliminated. The

process of an outlier and extreme values elimination decreased data from 125

to 63 samples. Multicollinearity test indicated in Appendix A (Table A.1)

that there is no strong correlation between independent variables in the

model. For another assumption of MLR such as independency of dependent

variables and nonperfect separation can be done while running the MLR.

Table 2 shows descriptive statistics of all independent variables in the

model; it shows that almost all of the variables distributed around their

mean values. Dependent variables category distribution is mostly populated

Table 2. Descriptive statistics.

N Minimum Maximum Mean

X1 DAR 63 0.3843 0.9100 0.676233 0.0177278 0.1407100

X2 ROA 63 0.0045 0.1100 0.040595 0.0035679 0.0283191

X3 Firm size 63 14.4590 19.3997 16.669130 0.1410517 1.1195630

X4 BI 63 0.0425 0.0975 0.063254 0.0016586 0.0131649

X5 JII 63 311.2800 759.0700 602.197302 12.789457 101.5131718

Valid N (listwise) 63

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in Category 3 (AAA-AA) by 31 samples followed by Category 2 (A) by 29

samples and Category 1 (BBB-D) by 3 samples (see Appendix A, Table A.2).

6.3. MLR result

6.3.1. Stepwise-predictive model

MLR stepwise results stated that firm size is the most significant variable

followed by ROA and DAR. While the BI rate and JII are excluded from the

model. The stepwise is using 2 log-likelihood test and chi-square test to

determine the significance of the variables. The null hypothesis in this test is

independent variable parameters in the model are equal to zero which means

having no effect on the dependent variable. We deny the null hypothesis due

to p-value < 0:05, which means the independent variable is significantly

affecting dependent variables.

Table 3 shows the result of the chi-square test and determined that firm

size, ROA, and DAR are all significantly affecting the dependent variable

Sukuk rating category. Though the stepwise result does do not provide the

necessary explanation on independent variables relationship toward the

dependent variable, this result constructs the predictive model and provides

proof for H1, H2, and H3.

6.3.2. Goodness-of-flt

The goodness-of-fit test indicates the goodness of the model in explaining the

dependent variable. The goodness-of-fit is indicated by model fitting infor-

mation (Table 4), the goodness-of-fit test, and pseudo R2 test.

Model Fitting Information is also called a global test which shows the

significance of all variables in the model. The null hypothesis in this test is all

parameters of independent variables equal to zero which means all

Table 3. Stepwise.

Model Action Effect (s) 2Log Likelihood Chi-Squarea df Sig.

0 Intercept 107.233 . 1 Entered X3 firmsize 85.908 21.325 2 0.000

2 Entered X2 ROA 72.532 13.376 2 0.001

3 Entered X1 DAR 59.720 12812 2 0.002

Stepwise Method: Forward Entry

Note: aThe chi-square for entry is based on the likelihood ratio test. Sources: Pefindo (2018); data processed.

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independent variables have no effect on the model. If p-value < 0:05 then

deny the null hypothesis. On the other hand, it means that all variables are

significantly affecting dependent variables simultaneously. The sig. equal

0.000 which means the null hypothesis denied and all independent variables

simultaneously affecting Sukuk rating. The result also means that the final

model consists of all independent variables that can explain the dependent

variable better than the intercept only model.

The goodness-of-the-Fittest indicates if the predictive result is large from

its observative result. Both Pearson and Deviance show sig. of 1.000 that

means the predictive result is not large from the observative result. This

result indicates excellent goodness-of-fit (Table 5).

Pseudo R2 indicates the goodness-of-fit of the model (Table 6). There are

two ways of interpretation of pseudo R2. First, pseudo R2 is considered as R2

that means this model can explain the Sukuk rating category by 53%, 64.8%,

and 44.3%. Second, pseudo-R2 is considered as the linear convergence of

predictive function and observative function which means that the linear

convergence in this model reached 53%, 64.8%, and 44.3%. Specifically, for

McFadden pseudo-R2, the excellent fit shows if pseudo R2 value is between

0.2 and 0.4 which shows the excellent fit in this model McFadden pseudo-R2

is 0.443.

Overall, all three indicators of goodness-of-fit are considered MLR model

in this study as a proper fit and are reliable to explain the dependent variable

Sukuk rating category.

Table 5. Goodness-of-fit.

Chi-Square df Sig.

Sources: Pefindo (2018); data processed.

Table 4. Model fitting information.

Model Fitting Criteria Likelihood Ratio Tests

Model 2 Log Likelihood Chi-Square df Sig.

Intercept Only 107.233 Final 59.720 47.513 6 0.000

Sources: Pefindo (2018); data processed.

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6.3.3. Significance test

The significance test uses the likelihood ratio test and parameter estimate to

configure the regression equation. The likelihood ratio test has already been

interpreted in the stepwise while constructing the predictive model. It is

more important to interpret the parameter estimate that employed theWald

test which indicates the relationship of independent variables toward de-

pendent variables categories.

Table 7 shows the coefficient in the regression equation and theWald test.

The regression equation is as follows:

Logit equation (Category 1/Category 3) Category 1 compared to Category

3 ¼ 10:547 34:159 dar.

Logit equation (Category 2/Category 3) Category 2 compared to Category

3 ¼ 43; 351 58; 821 roa 2; 358 firm size.

Norton et al. (2018) explain that the most important interpretation in

parameter estimates is the odds ratio, Exp(B). The odds ratio indicates how

powerful independent variables affect the dependent variable but firstly

measuring its significance by the Wald test. In Category 1, compared to

Category 3, the only significance occurred in DAR variable with odds ratio

value equal 1:462 1015 which means every increase in DAR level will

Table 6. Pseudo R-square.

Source: Pefindo (2018); data processed.

Table 7. Parameter estimates.

1 Intercept 10.547 0.162 0.687

X1 DAR 34.159 3.951 0.047 1.462E15

X2 ROA 0.573 0.000 0.988 1.773

X3 firmsize 0.356 0.047 0.828 1.428

2 Intercept 43.351 17.009 0.000

X1 DAR 2.610 0.598 0.440 0.074

X2 ROA 58.821 9.404 0.002 2.847E-26

X3 firmsize 2.358 15.842 0.000 0.095

Note: aThe reference category is: 3. Sources: Pefindo (2018); data processed.

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decrease the occurrence of Category 1 compared to Category 3 decreased by

1:462 1015 time. In Category 2 compared to Category 3, ROA and firm

size found to be significant and increases in both variable values will decrease

the occurrence of Category 2 compared to Category 3 by 2:847 1026 and

0.095 times, respectively.

In the overall result, all independent variables are favorable for Category

3. The increase in DAR will rather bring the Sukuk rating toward Category 3

than Category 1. These findings can be understood due to PEFINDO is also

considering the credit enhancement and DAR level can confirm the firm’s

capability of credit enhancement. PEFINDO stated that the higher the

credit rating, the higher the credit enhancement needed. While in Category

2 compared to Category 3, increases in firm size and ROA will reward the

firm a higher Sukuk rating. Firm size indicating character, capital, and

collateral of 5C, the higher the value the better it can represent the 5C

mentioned.While ROA represents the capacity, an increase in ROAmeans a

better capacity firm had in creditworthiness.

6.3.4. Classification table

Table 8 shows the predictive accuracy of the MLR model. In all samples

prediction, MLR predicts correctly 79.4%. Type I error occurred 7 times and

type II error occurred 6 times. Type I error is when the predictive rating is

higher than the observative rating and type II error is when the predictive

rating is lower than the observative rating. Arundina et al. (2015) stated that

satisfaction of MLR predictive accuracy can be measured by proportion by

chance accuracy derived from casing process summary distribution and an

increase of 25% in performance. Proportion by-chance accuracy for this

model is 56.996% (1:25ð0:0482 þ 0:462 þ 0:4922)). A comparison between

the predictive accuracy and proportion by chance accuracy shows that MLR

predictive accuracy is satisfying.

Observed 1 2 3 Percent Correct (%)

1 2 0 1 66.7 2 0 23 6 79.3 3 0 6 25 80.6 Overall percentage 3.2% 46.0% 50.8% 79.4

Sources: Pefindo (2018); data processed.

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6.4.1. How the ANN model is constructed

The first is to determine the independent variables in the ANN test. Selec-

tion of variables based on the previous MLR test. From the MLR test, there

are five independent variables determined by the process of Stepwise For-

ward Entry and only 3 that affect the Sukuk rating, namely DAR (X1), ROA

(X2), and firm size (X3). Then the three variables will be used in the ANN

model.

Next, determine the proportion of the sample to be used at each test

stage. Based on the basic Matlab settings, of the 63 samples, 70% were used

at the training stage, 15% were used at the validation stage, and the

remaining 15% was used at the test stage.

Before entering the training phase it is necessary to first determine the

structure of the ANN. At this stage the determination of the number of

neurons is only done at the hidden layer, the number of neurons can be

adjusted or can be changed according to the needs of the model and the

expected prediction results.

In the first part in Fig. 1, the input consists of 3 neurons namely each

independent variable, DAR (X1), ROA (X2), and firm size(X3). In the sec-

ond part, the hidden layer contains 5 neurons that will receive input and use

the transit transfer function. In the third part, the output layer contains 3

neurons according to the number of Sukuk rating categories and uses the

transfer function softmax to classify the input of hidden layers into catego-

ries. In the fourth part, the output shows the predicted results in the form of

Sukuk rating from the input the given.

On the ANN training results in Fig. 2, it can be seen that the training

process was stopped on the 24th iteration. Termination is carried out re-

ferring to the validation failure as many as 6 times in a row. At the time of

Fig. 1. ANN Matlab structure.

Source: Processed data, 2018.

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stopping, the gradient value is 0.009663. Based on the exercise performance

curve, you can see the blue line which is the development of the training

process until the dismissal. From the blue line, it can be seen that the ANN

training process is progressing well with values cross-entropy continuing to

decline. The best validation performance occurred in the 18th iteration with

a cross-entropy value of 0.10724.

From the training, the process has been generated bias values and weights

at each layer (Tables 9 and 10).

At the validation and test, there are two different stages. At the validation

stage, the trained network is measured at the level of generalization and stops

the training stage when the increase in network generalization stops. Mean-

while, at the test stage, it will not change the network being trained or after

experiencing a measurement of the level of generalization at the validation

Fig. 2. Training state and performance.

Source: Processed data, 2018.

Neuron Hidden Layer (NHL)

NHL1 1.1604 0.7611 0.2052 3:3136

NHL2 1:0849 1.9927 1.4795 1.4795 1.9830

NHL3 1:6654 1:7067 0:9887 3.0644

NHL4 2:1825 0:8273 2:2592 1:1171

NHL5 1:9930 1:5798 2.3628 1:3847

Source: Processed data, 2018.

The Validity of MLR and ANN in Predicting Sukuk Rating

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stage. At the test stage, the network will be tested independently to measure

the performance of the network that has been trained and validated.

At the training stage in Fig. 3 (see also Appendix A, Table A.3), ANN

correctly predicts 1 of 2 samples in Category 1 used in the training phase or

Table 10. Bias and weight of output layer.

Neuron Output Layer (NOL)

ZERO1 0.0293 0.9987 0.3458 0.4306 2.1291 1.5837

ZERO1 1.33967 1.1107 0.44897 2.4234 1.3865 1.3796

ZERO1 2.3576 0.6981 1.5311 0.8611 2.1507 0.4422

Source: Data processed, 2018.

Fig. 3. Confusion matrix.

Source: Processed data, 2018.

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by 50%, In Category 2, ANN successfully predicts 18 out of 21 samples or 85,

7% of all samples in Category 2. In Category 3, ANN managed to predict 18

out of 22 samples or 81.8% of all samples in Category 2. Overall the training

phase, ANN managed to predict 37 out of 45 samples or 82.2% of all samples

used in the training phase.

In the matrix, it confusion validation can be seen in Fig. 3 that ANN

successfully predicts 1 in 1 sample in Category 1 that was tested at the

validation stage or ANN has a 100% prediction accuracy rate in samples

from Category 1 that were tested at the validation stage. ANN successfully

predicted exactly 1 of 2 samples that were members of Category 2 or 50% of

all samples in Category 2 that were tested at the validation stage. ANN

successfully predicted exactly 6 of the 6 samples that were members of

Category 3 or 100% of all samples in Category 3 that were tested at the

validation stage. Overall, ANN can correctly predict 8 out of 9 samples or

88.9% of all samples tested at the validation stage.

At the test stage in Fig. 3, ANN does not have a sample of category 1

members tested so the level of accuracy is unknown. In Category 2, the

accuracy of ANN prediction is 66.7% or managed to predict 4 of the 6

samples tested. In Category 3, the accuracy of ANN prediction is 100% or 3

of the 3 samples tested. Overall the test phase, ANN has a prediction ac-

curacy of 77.8% or true in 7 of the 9 samples tested at the test stage.

The results of the three steps are summarized in one matrix confusion

final in Fig. 3 that shows ANN performance in all test samples. In Category

1, ANN managed to predict 2 out of 3 samples or an accuracy rate of 66.7%.

In Category 2, ANN managed to predict 23 out of 29 samples or an accuracy

rate of 79.3%. In Category 3, ANN succeeded in predicting 27 of 31 samples

or a prediction accuracy of 87.1%. Overall, ANN successfully predicted 52

out of 63 samples and an accuracy rate of 82.5%. From all stages, there were

7 errors Type I and 4 errors Type II.

6.4.2. The accuracy of the ANN model

ANN is used as the predictive model to perform rating prediction. There are

four predictive accuracy results that represent each of the three stages and

all stages of summary. This study will use the indicators in the validation

stage, as previous studies did, and all stages summary as authors argue as

more proper comparison by sample numbers. Matrix confusion is showing

the predictive accuracy, validation stages recorded 88.9% accuracy from all

nine samples tested in this stage. As for all stages summary: training,

The Validity of MLR and ANN in Predicting Sukuk Rating

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validation, and test, the predictive accuracy is 82.5%. In all stage summary,

there are 7 types I errors and 4 types II errors.

6.5. Predictive accuracy

In the last stage of this study’s analysis, predictive accuracy comparison

between MLR model and ANN model is conducted to determine which

method performs better predictive accuracy. MLR predictive accuracy is

79.4% of all samples and having 7 types I errors and 6 types II errors. While

ANN validation test predictive accuracy is 88.9% and has only 1 type I error.

The all stages summary of ANN predictive accuracy is 82.5% and having 7

types I error and 6 type II error. Comparing MLR to ANN both validation

and all stages summary produce the same result that ANN performs better

predictive accuracy than MLR, H6 is proven. As stated before, this finding is

also supported by previous studies that ANN performs better than methods

compared to it. It is because ANN is a more complex method and can

manage to adapt to all levels of problems.

7. Conclusion

The issue of Sukuk rating emerged as the Sukuk market developed. This

study investigates the determinants of Indonesian Sukuk rating and plot

predictive analysis comparing the ANN and MLR model. MLR stepwise

used to build a predictive model that results in DAR, ROA, and firm size as

a determinant of Sukuk rating. The predictive analysis results in ANN

predictive accuracy better MLR’s. Findings in this study confirmed that

higher credit enhancement, higher profitability, and a bigger size of firms

relate to higher Sukuk rating.

8. Recommendation

Authors recommendation for the inventor and issuer to conduct an indepen-

dent valuation to Sukuk rating using DAR (debt), ROA (profitability), and

firm size. Sukuk issuer can benefit from this study to perform better on those

significant variables to gain a higher Sukuk rating. Recommendation for up-

coming studies, researchers can further investigate more characteristic of

Sukuk itself in the Indonesian Sukuk market, such as Sukuk type, guarantee

status, other macroeconomic factors, and may include another financial ratio.

The results of this study with the model offered are highly recommended

for use in other places such as Southeast Asia, South Asia, the Middle East,

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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Europe, especially in the UK. In these regions, the development of Sukuk is

quite fast.

Acknowledgment

The authors are grateful and deeply indebted to Ati Harianti, S. E, MBA

from Universitas Trilogi for her contribution to an early version of this work.

All remaining errors are attributable to the authors.

Appendix A

X1 DAR X2 ROA X3 firmsize X4 BI X5 JII

X1 DAR Pearson Correlation 1 0.320 0.452 0.074 0.116

Sig. (two-tailed) 0.010 0.000 0.565 0.367

N 63 63 63 63 63

X2 ROA Pearson Correlation 0.320 1 0.600 0.162 0.155

Sig. (two-tailed) 0.010 0.000 0.204 0.226

N 63 63 63 63 63

X3 firmsize Pearson Correlation 0.452 0.600 1 0.244 0.440

Sig. (two-tailed) 0.000 0.000 0.054 0.000

N 63 63 63 63 63

X4 BI Pearson Correlation 0.074 0.162 0.244 1 0.548

Sig. (two-tailed) 0.565 0.204 0.054 0.000

N 63 63 63 63 63

X5 JII Pearson Correlation 0.116 0.155 0.440 0.548 1

Sig. (two-tailed) 0.367 0.226 0.000 0.000

N 63 63 63 63 63

Note. ** and * denote significance at 1% and 5%, respectively.

Table A.2. Table case processing summary.

N Marginal Percentage (%)

Y sukukrate 1 (BBB-D) 3 4.8 2 (A) 29 46.0 3 (AAA-AA) 31 49.2

Valid 63 100.0 Missing 0 Total 63 Subpopulation 63a

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The Validity of Multinomial Logistic Regression and Artificial Neural Network in Predicting Sukuk Rating: Evidence from Indonesian Stock Exchange

1. Introduction

5.5. JII X5

5.6. Predictive accuracy

6.5. Predictive accuracy

Muhammad Luqman Nurhakim

Zainul Kisman*

Faizah Syihab

Published 2 November 2020

The Sukuk (shariah bond) market is developing in Indonesia and potentially will capture the global market in the future. It is an attractive investment product and a hot current issue in the capital market. Especially, the problem of predicting an accurate and trustworthy rating. As the Sukuk market developed, the issue of Sukuk rating emerged. As ordinary investors will have difficulty predicting their ratings going forward, this research will provide solutions to the problems above. The objective of this study is to determine the Indonesian Sukuk rating determi- nants and comparing the Sukuk rating predictive model. This research uses Arti- ficial Neural Network (ANN) and Multinomial Logistic Regression (MLR) as the predictive analysis model. Data in this study are collected by purposive sampling and employing Sukuk rated by PEFINDO, an Indonesian rating agency. Findings in this study are debt, profitability and firm size significantly affecting Sukuk

*Corresponding author.

Review of Pacific Basin Financial Markets and Policies Vol. 23, No. 4 (2020) 2050032 (24 pages) °c World Scientific Publishing Co.

and Center for Pacific Basin Business, Economics and Finance Research DOI: 10.1142/S0219091520500320

rating category and the ANN performs better predictive accuracy than MLR. The implications of the results of the research for the issuer and bondholder are a higher level of credit enhancement, a higher level of profitability, and the bigger size of firm rewarding higher Sukuk rating.

Keywords: Sukuk rating; forecasting models; artificial neural network; multinomial logistic regression.

JEL Classifications: G1, C45, C52, C53

1. Introduction

August 2018, the accumulative amount of corporate Sukuk issuance raised

from IDR 26,394.90 billion to IDR 30,933.40 billion. Growth during the six-

month period recorded at 17.19%, Indonesia’s Authority of Financial Service

(OJK) stated in its report. Standing Committee for Economic and Com-

mercial Cooperation of the Organization of Islamic Cooperation (COMCEC)

stated in its report on Sukuk market development in 2018 that the Indo-

nesian Sukuk market is currently considered as developing market and yet it

has a significant potential to capture global Sukuk market share in the future

(COMCEC, 2018). Sukuk itself is popularly known as shariah bond, though

in fact, both Sukuk and bond is basically and fundamentally different.

COMCEC research report explained that Sukuk is not an interest-bearing

financial as the way bond is but it possesses a similar function as a financial

instrument in the money market (COMCEC, 2018).

According to Giap et al. (2018), in spite of the positive development

execution of Indonesia in the course of recent decades, concerns have been

communicated about whether the nation would be trapped in a middle-

income trap. So, this study believes industry financing using Sukuk is a

solution so that the country can get out of a middle-income trap.

Moreover, according to Khartabiel et al. (2019), companies do not have to

worry about issuing Sukuk because, in the postcrisis period (2008), the

market reaction for Sukuk is positive and significant, apparently due to new

market participants’ views, awareness and increased demand for Islamic

financial products, whereas the conventional bonds do not have a significant

market reaction. This is why discussions about Sukuk are important, espe-

cially for Indonesia and other developing countries about how to accurately

predict ratings.

Kartiwi et al. (2018) stated the development of Sukuk emerged issues on

Sukuk rating that shows the issuer’s creditworthiness. Indonesia’s Rating

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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Agency (PEFINDO) explained in its release that credit rating is indicating

the issuer’s capacity to fulfill long-term financial commitment under shariah

principles contract. This issue on Sukuk rating is not only about what Sukuk

rating one issuer is but also factors that determine the issuer’s rating. The

later mentioned issue is highly discussed in Sukuk field research mostly in

the mature Sukuk market country, Malaysia. The main problem in rating

issue is rating agency cannot be widely transparent on what factor people

need to know unless the final result, rating. Rating agencies limited access to

detailed rating methodology and people found this to be too complicated to

understand and according to DeBoskey and Gillett (2011) felt the lack of

corporate transparency. Then, Chu et al. (2019) noted the results of his

research that increased transparency of information can reinforce invest-

ment certainty and lead to fewer forecast errors.

This research’s objective is to give a better approach toward Sukuk rating

understanding for the common investor. A better approach can be provided

by using the most popular factors that can be easily recognized. Factors

involved will be tested for its significance to build a predictive model of

Sukuk rating. The predictive model will be tested in both multinomial lo-

gistic regression and artificial neural network than comparing their predic-

tive accuracy. Findings in this study hopefully can provide a better and

simplified approach for Indonesian Sukuk investors.

2. Theoretical Framework

2.1. Sukuk

Sukuk’s origin from the Arabic word \sack" literally means cheque or cer-

tificate. As for Borhan and Ahmad (2018), Sukuk is all form of intention as a

contract symbol or transferring rights, debt, or money. Ahmed et al. (2014)

stated that Sukuk is a certificate of equal value that represents an undivided

share on ownership of tangible assets, services, a certain project, or in-

vestment. As stated before, Sukuk is popularly known as shariah bond.

COMCEC reported that Sukuk is a financial instrument in the market as an

answer to the needs of shariah compliance instruments that work similarly to

a bond (COMCEC, 2018). Shariah compliance instruments must obey

shariah principles to avoid riba, gharar, maysir, injustice, and the activity of

investment must be permitted by shariah (Dusuki, 2012).

There are differences between Sukuk and bond. Mseddi and Naifar (2013)

stated Table 1 that bond is a pure debt contract between investor and issuer

that issuer uses to finance all kinds of business activity and valued based on

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the issuer’s credit worthiness. While, Sukuk is a certificate of trust that

represent ownership interest, specific assets, specific services, or project that

certified by the third party. Sukuk equaling bond’s function as it gives return

and paid at due. The differences that separate Sukuk and bond fundamen-

tally are the underlying for the contract, the relationship between investors

and issuers, and sale price. Bond is based on the loan, while Sukuk must not

be based on the loan. Sukuk’s underlying must comply with Shariah prin-

ciples and depends on the type of Sukuk issued. The relationship in the bond

is definitely debts relationship, borrowers and lenders. Relationship in Sukuk

will depend on its underlying and type of contract, in Mudharabah Sukuk

the relationship is a partnership. Then the bond can be sold on premium or

discount, while Sukuk must be sold at its fair value.

There are so many Sukuk classifications, yet some literature used the

asset-based and asset-backed classification. The Securities Commission

Malaysia report stated that this classification is due to its technical and

commercial features. The difference between these two types of Sukuk is

mainly on how underlying assets treated as Sukuk must have underlying

assets. Asset-based Sukuk is occurring when there is no true sale of assets to

Table 1. Sukuk and bond.

Differences Sukuk Bond

Ownership Clearly regulated Holder rightful of cash flow from pure debt

The contract between issuer and holder

Based on financing or certain business

Purely getting money from money

Underlying asset nature and usage

Shariah compliance As long as not against the jurisdiction

Operation of sale Sale of assets, investment, or project

Sale of debt

Expense on assets Probably stick to Sukuk holders None Securitization Price Based on its underlying assets

fair value Depends on issuer’s credit

worthiness Risk and return Explicit share on risk and return

based on profit generated by underlying assets

Holders endure low risk and return based on the coupon

Instrument trading Depend on underlying assets nature

No prohibition

No prohibition

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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investors, which means that the assets remain in the issuer’s balance sheet.

Whilst-backed Sukuk is occurring when there is true sale. The ownership of

assets is legally transferred into investors. Literatures stated that the main

different between these two types of Sukuk is significant when default occurs

in Herzi (2016) and Rachmawati and Ghani (2015). Asset-backed is pref-

erable at default, this type is more secure than asset-based in these cir-

cumstances. Asset-based investors can sell the assets when default. On the

other hand, asset-based ultimate recourse at default is the buyback clause.

Therefore, asset-based highly considers the issuer’s creditworthiness.

Indonesian corporate Sukuk does not vary in the market, though there are

so many types of contracts in Sukuk issuance. COMCEC report stated that

based on the National Shariah Board (DSN) data on Sukuk issuance in 2016,

corporate mainly issued ijarah and mudharabah type of Sukuk (COMCEC,

2018). Indonesian Directorate of Shariah Finance defined Sukuk ijarah as a

type of Sukuk that based on the ijarah contract. The underlying of Sukuk

ijarah is the asset that its beneficial ownership is sold to investors. The

underlying assets will remain in obligor’s possession and obligor obliged to

pay the investor the rent for the use of underlying assets. Obligor then buys

this underlying asset back at its fair value as due. Indonesian Directorate of

Shariah Finance stated that Sukuk mudharabah is the type of Sukuk based

on the mudharabah contract. The relationship between investors and issuer

is a partnership where investor as the capital provider and as the one that

works on the investment project. Sukuk mudharabah will divide profit

gained from the investment project based on the agreement and loss will be

entirely investors exposure.

2.2. Sukuk rating

Sukuk rating, aforementioned, is indicating the issuer’s capacity to fulfill its

long-term financial commitment under shariah contract. PEFINDO rating

agency revealed its rating process in its release on securitization that found

to be complicated to understand. The release stated the type of analysis in

rating Sukuk. In short, the rating methodology analyzes risk, credit en-

hancement, assets, assets management, and cash flows to classify the issuer’s

rating. Though the analysis process was briefly described, it remains unclear

what should be concerned in rating issues. The rating analysis is as follows:

(1) An industry analysis conducted to investigate the characteristics and

risk profile of an industry that relates to assets in many aspects.

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(2) Determine \Benchmark Pool", industry analysis result used to deter-

mine the benchmark pool that PEFINDO uses to measure risk factors of

assets.

(3) Determine \Base Default Frequency (BDF)", purposed to measure ex-

pectancy level on loss and credit enhancement for each rating category.

The higher the rating, securitization needs higher credit enhancement.

Nonperforming Loan (NPL) is a factor to determine the BDF value.

(4) Servicer Evaluation, stage of evaluating the capability of the servicer in

managing securitized assets.

using benchmark pool and BDF.

(6) Securitization structure analysis assessing the risk profile of securitiza-

tion transaction structure by evaluating security scheme, security

agreement analysis, protection on credit risk, legal aspect, and audit

result analysis.

(7) Cash flow analysis, measuring cash flow adequacy generated by securi-

tized assets compare to expenses.

2.3. 5C of credit

Sukuk rating indicates the issuer’s capacity that relates to the issuer’s cred-

itworthiness. Creditworthiness is also found important in Sukuk, whereas

asset-based Sukuk holder relies only on obligor’s creditworthiness since

the underlying assets remain on obligor’s balance sheet. Peprah et al.

(2017) explained that creditworthiness assessed by 5C principles of credit, as

follows:

analysis mainly investigates borrowers’ good will to repay debt.

(2) Capital, very important analysis to measure borrower’s capability to

endure market and unexpected risk.

(3) Capacity, Sharma and Kalra (2015) capacity is an assessment of bor-

rower’s capability to repay debt.

(4) Collateral, purposed to secure financial exposure in case of default.

(5) Condition, analysis of debt purposes, industry, economy, and political

environment.

3. Literature Review

Studies on Sukuk have been growing in numbers since the development of

the Sukuk market around the globe, though quite a few Sukuk rating

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studies. Most studies on Sukuk rating employed in Bursa Malaysia as its

Sukuk market considered at a mature stage, as per the COMCEC report.

Variables in Sukuk rating studies vary but commonly most studies used

financial ratio, macroeconomic factors, and Sukuk itself (COMCEC,

2018). Methodology on Sukuk rating studies also varies though most of the

studies used predictive analysis such as multinomial logistic regression and

ordered logistic regression.

Arundina and Omar (2009) and Borhan and Ahmad (2018) tried to

examine the Sukuk rating determinant in Bursa Malaysia. Analysis of this

study is based on multinomial logistic regression findings and resulted in

the significance of profitability and guarantee status. The influence of

significant factors is all positive toward the Sukuk rating. Firm size is not

a significant factor, though Borhan and Ahmad (2018) stated that firm

size is the prime factor in the Sukuk rating study. Smaoui and Khawaja

(2018) investigated Sukuk’s market development determinant. Interest

spread, the difference between borrowing and lending rate, found to be

negatively influencing Sukuk market development. Elhaj et al. (2015)

found in their study that board size, financial leverage, profitability, firm

size, and Sukuk structure influenced Sukuk’s rating. Elhaj et al. (2015)

found the negative influence of financial leverage represented by debt to

total assets ratio (DAR). Arundina et al. (2015) compared neural network

inferences and multinomial logistic regression in predictive accuracy re-

search on Malaysian Sukuk rating. This study claimed that neural net-

works better logit predictive accuracy. This study also found return on

assets (ROA) and DAR significant. Naifar and Mseddi (2013) showed in

their study that Sukuk yield reacts positively toward stock return index.

4. Methodology

4.1. Data and sample

Data in this study are secondary data taken from various related sources.

Sukuk rated by PEFINDO will be this study’s sample and a sample must

contain all variables value. Sources in this study are PEFINDO releases on

rating, firm’s financial statement, Indonesian stock exchange (IDX), and

Indonesia’s Central Bureau of Statistics (BPS). There are 125 samples col-

lected and filtered by these criteria and issued outlier data and extreme

values used become 63 samples.

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(MLR) used to predict categorical placement or probability of categorical

membership on a dependent variable based on a few independent variables.

MLR is a simple development of binary logistic regression that allows more

than 2 categories dependent variable. MLR equation is as follows:

log pðgroupjÞ pðgroupiÞ ¼ m þ i1X1 þ i2X2 þ i3X3 þ þ inXn :

MLR uses maximum likelihood estimation that maximizes the probability of

dependent variable occurrence by finding a regression coefficient. MLR

assumes the dependent variable category should be independent, multi-

collinearity test, no extreme values or outlier, and nonperfect separation.

There will be two general tests inMLR, the goodness of fit test and significance

test. The goodness-of-fit test provided with three indicators which are2 log-

likelihood test, chi-square test, and pseudoR2.2 log-likelihood will compare

the final model consists of all independent variables against the intercept and

only model. The chi-square test indicates the deviation of predictive proba-

bility against its observed value. Pseudo R2 is said to be R2 and yet it is not

realR2 instead PseudoR2 is the measurement of linear convergence between

the predictive probability and the observation probability. The significance

test will be the partial test and the Wald test. The partial test is indicating

the influence of one independent variable toward the dependent variable.

Wald test will describe the relationship between the independent variable

and the dependent variable’s category. This study will do the predictive test

which will measure MLR model predictive accuracy.

4.3. Arti¯cial neural network

Sena (2017) explains that Artificial Neural Network (ANN) is a nonpara-

metric predictive analysis which imitates the work of human brains. ANN is

part of machine learning, artificial intelligence, and also known as a multi-

layer perceptron. According to Kumar and Haynes (2003), ANN is suc-

cessfully used in financial fields, such as stock price prediction, portfolio

management and selection, and credit rating analysis. Matlab provides types

of ANN that produce different output and ANN Pattern Recognition is

launched to conduct the predictive analysis. ANN Pattern Recognition’s

output is categorical that complies with the study objective to predict the

rating of Sukuk. ANN in Matlab has three stages of test: training, validation,

and test. In the training stage, ANN learned and change weight and bias in

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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the network. In the Validation stage, ANN will be generalized to its opti-

mum level that there will be no better performance possible to achieve. In

the test stage, the model will be tested with no effect that increases ANN

performance. Most of the studies using ANN and Matlab indicate that the

prime performance indicator extracted from the validation stage. Two main

indicators are cross-entropy or error degree and confusion matrix that show

predictive accuracy. This study will compare ANN predictive accuracy and

MLR predictive accuracy.

5. Hypothesis

This study tries to find determinants of Sukuk rating by plotting financial

ratios and macroeconomic factors. Independent variables will be elaborate as

follows.

5.1. DAR X1

According to Erica (2018), Gibson (2013) and Gitman and Zutter (2015)

that debt to total assets ratio is the measurement of risk but also a financial

leverage ratio that shows a potential profit in the future. Elhaj et al. (2015),

Arundina et al. (2015) and Pebruary (2016) found DAR significantly af-

fecting Sukuk rating in a negative way. DAR not only represents financial

leverage ratio but also capital in 5C, therefore authors believe that DAR will

significantly affect Sukuk rating.

5.2. ROA X2

Erica (2018), Gibson (2013) and Gitman and Zutter (2015) define that re-

turn on assets represents profitability that shows the capability to generate

profit by the firm’s total assets. Borhan and Ahmad (2018), Elhaj et al.

(2015), Arundina et al. (2015) revealed a positive significant influence of

ROA toward Sukuk rating. Borhan and Ahmad (2018) stated that higher

profitability rewarded by higher Sukuk rating. ROA is also representing

capacity in 5C that ensure issuers to pay their liabilities.

H2: ROA significantly affecting Sukuk’s rating.

5.3. Firm size X3

Firm size is generally measured by total assets in natural logarithm form.

Borhan and Ahmad (2018) stated that there is no significant influence of firm

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size, despite firm size being considered as prime factors in Sukuk rating

studies. While Elhaj et al. (2015) found positive influence by firm size toward

Sukuk rating. Firm size can represent character, capital, and collateral of

5C. The character can be represented as firm size measured by total assets

that show the value of the firm, the higher value means bigger firm and such

big firm will behave as expectedly as explained by Setiadharma and Machali

(2017). This reason is also why it can represent capital that shows the ca-

pability of risk-bearing and collateral as the big firm has more alternatives to

pay liabilities.

5.4. Bank Indonesia (BI) rate X4

BI rate in this study is BI 7 day repo rate that Bank of Indonesia defined as

monetary policy effectively and quickly affects the money market. Smaoui

and Khawaja (2018) found interest spread negatively affect Sukuk market

development. BI rate is considered a macroeconomic factor and represents

the condition of 5C that will significantly affect the Sukuk rating.

H4: BI rate significantly affecting Sukuk rating.

5.5. JII X5

JII stands for Jakarta Islamic Index, JII listed 30 most liquid shariah stock in

the market. Sclip et al. (2016) found a high volatility relationship between

the international stock index and the Sukuk market in the financial crisis.

Naifar and Mseddi (2013) stated that Sukuk yield reacted positively against

the stock return index in Malaysia. As well as BI rate, JII is also considered

as a macroeconomic factor that represents the condition of 5C and will

significantly affect Sukuk rating.

5.6. Predictive accuracy

Arundina et al. (2015) found that Neural Network Inferences better MLR

performances in Malaysian Sukuk rating predictive analysis. Kumar and

Haynes (2003) found that ANN is better that discriminant analysis in pre-

dicting bond rating. ANN is considered a more complex model than MLR

and can suit the complexity level of models.

H6: ANN predictive accuracy higher than MLR predictive accuracy.

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6.1. Introduction

The objective of this study is to find the determinants of Indonesian Sukuk

rating and to decide which method has better predictive accuracy. First, the

authors construct the predictive model which only included the significant

independent variables as described by Widarjono (2015). All independent

variables are continuous variables. While the dependent variable is cate-

gorical. The authors divide the Sukuk rating into three categories: 1, 2, and

3. Category 1 is for BBB and below Sukuk rating, Category 2 is for A Sukuk

rating, and Category 3 is for AA and AAA Sukuk rating. Model predictive

will be selected by launching a stepwise MLR test that enters only the

significant variables and excluded nonsignificant variables. This is due to the

inability of ANN to figure the effective variables to affect the dependent

variables. In order to do so, authors, as aforementioned, conduct stepwise

MLR as a more reliable procedure to construct a predictive model.

6.2. MLR assumption test

The assumption test is necessary to build a good and reliable MLR model.

Therefore, outliers and extreme values in the model must be eliminated. The

process of an outlier and extreme values elimination decreased data from 125

to 63 samples. Multicollinearity test indicated in Appendix A (Table A.1)

that there is no strong correlation between independent variables in the

model. For another assumption of MLR such as independency of dependent

variables and nonperfect separation can be done while running the MLR.

Table 2 shows descriptive statistics of all independent variables in the

model; it shows that almost all of the variables distributed around their

mean values. Dependent variables category distribution is mostly populated

Table 2. Descriptive statistics.

N Minimum Maximum Mean

X1 DAR 63 0.3843 0.9100 0.676233 0.0177278 0.1407100

X2 ROA 63 0.0045 0.1100 0.040595 0.0035679 0.0283191

X3 Firm size 63 14.4590 19.3997 16.669130 0.1410517 1.1195630

X4 BI 63 0.0425 0.0975 0.063254 0.0016586 0.0131649

X5 JII 63 311.2800 759.0700 602.197302 12.789457 101.5131718

Valid N (listwise) 63

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in Category 3 (AAA-AA) by 31 samples followed by Category 2 (A) by 29

samples and Category 1 (BBB-D) by 3 samples (see Appendix A, Table A.2).

6.3. MLR result

6.3.1. Stepwise-predictive model

MLR stepwise results stated that firm size is the most significant variable

followed by ROA and DAR. While the BI rate and JII are excluded from the

model. The stepwise is using 2 log-likelihood test and chi-square test to

determine the significance of the variables. The null hypothesis in this test is

independent variable parameters in the model are equal to zero which means

having no effect on the dependent variable. We deny the null hypothesis due

to p-value < 0:05, which means the independent variable is significantly

affecting dependent variables.

Table 3 shows the result of the chi-square test and determined that firm

size, ROA, and DAR are all significantly affecting the dependent variable

Sukuk rating category. Though the stepwise result does do not provide the

necessary explanation on independent variables relationship toward the

dependent variable, this result constructs the predictive model and provides

proof for H1, H2, and H3.

6.3.2. Goodness-of-flt

The goodness-of-fit test indicates the goodness of the model in explaining the

dependent variable. The goodness-of-fit is indicated by model fitting infor-

mation (Table 4), the goodness-of-fit test, and pseudo R2 test.

Model Fitting Information is also called a global test which shows the

significance of all variables in the model. The null hypothesis in this test is all

parameters of independent variables equal to zero which means all

Table 3. Stepwise.

Model Action Effect (s) 2Log Likelihood Chi-Squarea df Sig.

0 Intercept 107.233 . 1 Entered X3 firmsize 85.908 21.325 2 0.000

2 Entered X2 ROA 72.532 13.376 2 0.001

3 Entered X1 DAR 59.720 12812 2 0.002

Stepwise Method: Forward Entry

Note: aThe chi-square for entry is based on the likelihood ratio test. Sources: Pefindo (2018); data processed.

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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independent variables have no effect on the model. If p-value < 0:05 then

deny the null hypothesis. On the other hand, it means that all variables are

significantly affecting dependent variables simultaneously. The sig. equal

0.000 which means the null hypothesis denied and all independent variables

simultaneously affecting Sukuk rating. The result also means that the final

model consists of all independent variables that can explain the dependent

variable better than the intercept only model.

The goodness-of-the-Fittest indicates if the predictive result is large from

its observative result. Both Pearson and Deviance show sig. of 1.000 that

means the predictive result is not large from the observative result. This

result indicates excellent goodness-of-fit (Table 5).

Pseudo R2 indicates the goodness-of-fit of the model (Table 6). There are

two ways of interpretation of pseudo R2. First, pseudo R2 is considered as R2

that means this model can explain the Sukuk rating category by 53%, 64.8%,

and 44.3%. Second, pseudo-R2 is considered as the linear convergence of

predictive function and observative function which means that the linear

convergence in this model reached 53%, 64.8%, and 44.3%. Specifically, for

McFadden pseudo-R2, the excellent fit shows if pseudo R2 value is between

0.2 and 0.4 which shows the excellent fit in this model McFadden pseudo-R2

is 0.443.

Overall, all three indicators of goodness-of-fit are considered MLR model

in this study as a proper fit and are reliable to explain the dependent variable

Sukuk rating category.

Table 5. Goodness-of-fit.

Chi-Square df Sig.

Sources: Pefindo (2018); data processed.

Table 4. Model fitting information.

Model Fitting Criteria Likelihood Ratio Tests

Model 2 Log Likelihood Chi-Square df Sig.

Intercept Only 107.233 Final 59.720 47.513 6 0.000

Sources: Pefindo (2018); data processed.

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6.3.3. Significance test

The significance test uses the likelihood ratio test and parameter estimate to

configure the regression equation. The likelihood ratio test has already been

interpreted in the stepwise while constructing the predictive model. It is

more important to interpret the parameter estimate that employed theWald

test which indicates the relationship of independent variables toward de-

pendent variables categories.

Table 7 shows the coefficient in the regression equation and theWald test.

The regression equation is as follows:

Logit equation (Category 1/Category 3) Category 1 compared to Category

3 ¼ 10:547 34:159 dar.

Logit equation (Category 2/Category 3) Category 2 compared to Category

3 ¼ 43; 351 58; 821 roa 2; 358 firm size.

Norton et al. (2018) explain that the most important interpretation in

parameter estimates is the odds ratio, Exp(B). The odds ratio indicates how

powerful independent variables affect the dependent variable but firstly

measuring its significance by the Wald test. In Category 1, compared to

Category 3, the only significance occurred in DAR variable with odds ratio

value equal 1:462 1015 which means every increase in DAR level will

Table 6. Pseudo R-square.

Source: Pefindo (2018); data processed.

Table 7. Parameter estimates.

1 Intercept 10.547 0.162 0.687

X1 DAR 34.159 3.951 0.047 1.462E15

X2 ROA 0.573 0.000 0.988 1.773

X3 firmsize 0.356 0.047 0.828 1.428

2 Intercept 43.351 17.009 0.000

X1 DAR 2.610 0.598 0.440 0.074

X2 ROA 58.821 9.404 0.002 2.847E-26

X3 firmsize 2.358 15.842 0.000 0.095

Note: aThe reference category is: 3. Sources: Pefindo (2018); data processed.

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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decrease the occurrence of Category 1 compared to Category 3 decreased by

1:462 1015 time. In Category 2 compared to Category 3, ROA and firm

size found to be significant and increases in both variable values will decrease

the occurrence of Category 2 compared to Category 3 by 2:847 1026 and

0.095 times, respectively.

In the overall result, all independent variables are favorable for Category

3. The increase in DAR will rather bring the Sukuk rating toward Category 3

than Category 1. These findings can be understood due to PEFINDO is also

considering the credit enhancement and DAR level can confirm the firm’s

capability of credit enhancement. PEFINDO stated that the higher the

credit rating, the higher the credit enhancement needed. While in Category

2 compared to Category 3, increases in firm size and ROA will reward the

firm a higher Sukuk rating. Firm size indicating character, capital, and

collateral of 5C, the higher the value the better it can represent the 5C

mentioned.While ROA represents the capacity, an increase in ROAmeans a

better capacity firm had in creditworthiness.

6.3.4. Classification table

Table 8 shows the predictive accuracy of the MLR model. In all samples

prediction, MLR predicts correctly 79.4%. Type I error occurred 7 times and

type II error occurred 6 times. Type I error is when the predictive rating is

higher than the observative rating and type II error is when the predictive

rating is lower than the observative rating. Arundina et al. (2015) stated that

satisfaction of MLR predictive accuracy can be measured by proportion by

chance accuracy derived from casing process summary distribution and an

increase of 25% in performance. Proportion by-chance accuracy for this

model is 56.996% (1:25ð0:0482 þ 0:462 þ 0:4922)). A comparison between

the predictive accuracy and proportion by chance accuracy shows that MLR

predictive accuracy is satisfying.

Observed 1 2 3 Percent Correct (%)

1 2 0 1 66.7 2 0 23 6 79.3 3 0 6 25 80.6 Overall percentage 3.2% 46.0% 50.8% 79.4

Sources: Pefindo (2018); data processed.

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6.4.1. How the ANN model is constructed

The first is to determine the independent variables in the ANN test. Selec-

tion of variables based on the previous MLR test. From the MLR test, there

are five independent variables determined by the process of Stepwise For-

ward Entry and only 3 that affect the Sukuk rating, namely DAR (X1), ROA

(X2), and firm size (X3). Then the three variables will be used in the ANN

model.

Next, determine the proportion of the sample to be used at each test

stage. Based on the basic Matlab settings, of the 63 samples, 70% were used

at the training stage, 15% were used at the validation stage, and the

remaining 15% was used at the test stage.

Before entering the training phase it is necessary to first determine the

structure of the ANN. At this stage the determination of the number of

neurons is only done at the hidden layer, the number of neurons can be

adjusted or can be changed according to the needs of the model and the

expected prediction results.

In the first part in Fig. 1, the input consists of 3 neurons namely each

independent variable, DAR (X1), ROA (X2), and firm size(X3). In the sec-

ond part, the hidden layer contains 5 neurons that will receive input and use

the transit transfer function. In the third part, the output layer contains 3

neurons according to the number of Sukuk rating categories and uses the

transfer function softmax to classify the input of hidden layers into catego-

ries. In the fourth part, the output shows the predicted results in the form of

Sukuk rating from the input the given.

On the ANN training results in Fig. 2, it can be seen that the training

process was stopped on the 24th iteration. Termination is carried out re-

ferring to the validation failure as many as 6 times in a row. At the time of

Fig. 1. ANN Matlab structure.

Source: Processed data, 2018.

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stopping, the gradient value is 0.009663. Based on the exercise performance

curve, you can see the blue line which is the development of the training

process until the dismissal. From the blue line, it can be seen that the ANN

training process is progressing well with values cross-entropy continuing to

decline. The best validation performance occurred in the 18th iteration with

a cross-entropy value of 0.10724.

From the training, the process has been generated bias values and weights

at each layer (Tables 9 and 10).

At the validation and test, there are two different stages. At the validation

stage, the trained network is measured at the level of generalization and stops

the training stage when the increase in network generalization stops. Mean-

while, at the test stage, it will not change the network being trained or after

experiencing a measurement of the level of generalization at the validation

Fig. 2. Training state and performance.

Source: Processed data, 2018.

Neuron Hidden Layer (NHL)

NHL1 1.1604 0.7611 0.2052 3:3136

NHL2 1:0849 1.9927 1.4795 1.4795 1.9830

NHL3 1:6654 1:7067 0:9887 3.0644

NHL4 2:1825 0:8273 2:2592 1:1171

NHL5 1:9930 1:5798 2.3628 1:3847

Source: Processed data, 2018.

The Validity of MLR and ANN in Predicting Sukuk Rating

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stage. At the test stage, the network will be tested independently to measure

the performance of the network that has been trained and validated.

At the training stage in Fig. 3 (see also Appendix A, Table A.3), ANN

correctly predicts 1 of 2 samples in Category 1 used in the training phase or

Table 10. Bias and weight of output layer.

Neuron Output Layer (NOL)

ZERO1 0.0293 0.9987 0.3458 0.4306 2.1291 1.5837

ZERO1 1.33967 1.1107 0.44897 2.4234 1.3865 1.3796

ZERO1 2.3576 0.6981 1.5311 0.8611 2.1507 0.4422

Source: Data processed, 2018.

Fig. 3. Confusion matrix.

Source: Processed data, 2018.

2050032-18

by 50%, In Category 2, ANN successfully predicts 18 out of 21 samples or 85,

7% of all samples in Category 2. In Category 3, ANN managed to predict 18

out of 22 samples or 81.8% of all samples in Category 2. Overall the training

phase, ANN managed to predict 37 out of 45 samples or 82.2% of all samples

used in the training phase.

In the matrix, it confusion validation can be seen in Fig. 3 that ANN

successfully predicts 1 in 1 sample in Category 1 that was tested at the

validation stage or ANN has a 100% prediction accuracy rate in samples

from Category 1 that were tested at the validation stage. ANN successfully

predicted exactly 1 of 2 samples that were members of Category 2 or 50% of

all samples in Category 2 that were tested at the validation stage. ANN

successfully predicted exactly 6 of the 6 samples that were members of

Category 3 or 100% of all samples in Category 3 that were tested at the

validation stage. Overall, ANN can correctly predict 8 out of 9 samples or

88.9% of all samples tested at the validation stage.

At the test stage in Fig. 3, ANN does not have a sample of category 1

members tested so the level of accuracy is unknown. In Category 2, the

accuracy of ANN prediction is 66.7% or managed to predict 4 of the 6

samples tested. In Category 3, the accuracy of ANN prediction is 100% or 3

of the 3 samples tested. Overall the test phase, ANN has a prediction ac-

curacy of 77.8% or true in 7 of the 9 samples tested at the test stage.

The results of the three steps are summarized in one matrix confusion

final in Fig. 3 that shows ANN performance in all test samples. In Category

1, ANN managed to predict 2 out of 3 samples or an accuracy rate of 66.7%.

In Category 2, ANN managed to predict 23 out of 29 samples or an accuracy

rate of 79.3%. In Category 3, ANN succeeded in predicting 27 of 31 samples

or a prediction accuracy of 87.1%. Overall, ANN successfully predicted 52

out of 63 samples and an accuracy rate of 82.5%. From all stages, there were

7 errors Type I and 4 errors Type II.

6.4.2. The accuracy of the ANN model

ANN is used as the predictive model to perform rating prediction. There are

four predictive accuracy results that represent each of the three stages and

all stages of summary. This study will use the indicators in the validation

stage, as previous studies did, and all stages summary as authors argue as

more proper comparison by sample numbers. Matrix confusion is showing

the predictive accuracy, validation stages recorded 88.9% accuracy from all

nine samples tested in this stage. As for all stages summary: training,

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validation, and test, the predictive accuracy is 82.5%. In all stage summary,

there are 7 types I errors and 4 types II errors.

6.5. Predictive accuracy

In the last stage of this study’s analysis, predictive accuracy comparison

between MLR model and ANN model is conducted to determine which

method performs better predictive accuracy. MLR predictive accuracy is

79.4% of all samples and having 7 types I errors and 6 types II errors. While

ANN validation test predictive accuracy is 88.9% and has only 1 type I error.

The all stages summary of ANN predictive accuracy is 82.5% and having 7

types I error and 6 type II error. Comparing MLR to ANN both validation

and all stages summary produce the same result that ANN performs better

predictive accuracy than MLR, H6 is proven. As stated before, this finding is

also supported by previous studies that ANN performs better than methods

compared to it. It is because ANN is a more complex method and can

manage to adapt to all levels of problems.

7. Conclusion

The issue of Sukuk rating emerged as the Sukuk market developed. This

study investigates the determinants of Indonesian Sukuk rating and plot

predictive analysis comparing the ANN and MLR model. MLR stepwise

used to build a predictive model that results in DAR, ROA, and firm size as

a determinant of Sukuk rating. The predictive analysis results in ANN

predictive accuracy better MLR’s. Findings in this study confirmed that

higher credit enhancement, higher profitability, and a bigger size of firms

relate to higher Sukuk rating.

8. Recommendation

Authors recommendation for the inventor and issuer to conduct an indepen-

dent valuation to Sukuk rating using DAR (debt), ROA (profitability), and

firm size. Sukuk issuer can benefit from this study to perform better on those

significant variables to gain a higher Sukuk rating. Recommendation for up-

coming studies, researchers can further investigate more characteristic of

Sukuk itself in the Indonesian Sukuk market, such as Sukuk type, guarantee

status, other macroeconomic factors, and may include another financial ratio.

The results of this study with the model offered are highly recommended

for use in other places such as Southeast Asia, South Asia, the Middle East,

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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Europe, especially in the UK. In these regions, the development of Sukuk is

quite fast.

Acknowledgment

The authors are grateful and deeply indebted to Ati Harianti, S. E, MBA

from Universitas Trilogi for her contribution to an early version of this work.

All remaining errors are attributable to the authors.

Appendix A

X1 DAR X2 ROA X3 firmsize X4 BI X5 JII

X1 DAR Pearson Correlation 1 0.320 0.452 0.074 0.116

Sig. (two-tailed) 0.010 0.000 0.565 0.367

N 63 63 63 63 63

X2 ROA Pearson Correlation 0.320 1 0.600 0.162 0.155

Sig. (two-tailed) 0.010 0.000 0.204 0.226

N 63 63 63 63 63

X3 firmsize Pearson Correlation 0.452 0.600 1 0.244 0.440

Sig. (two-tailed) 0.000 0.000 0.054 0.000

N 63 63 63 63 63

X4 BI Pearson Correlation 0.074 0.162 0.244 1 0.548

Sig. (two-tailed) 0.565 0.204 0.054 0.000

N 63 63 63 63 63

X5 JII Pearson Correlation 0.116 0.155 0.440 0.548 1

Sig. (two-tailed) 0.367 0.226 0.000 0.000

N 63 63 63 63 63

Note. ** and * denote significance at 1% and 5%, respectively.

Table A.2. Table case processing summary.

N Marginal Percentage (%)

Y sukukrate 1 (BBB-D) 3 4.8 2 (A) 29 46.0 3 (AAA-AA) 31 49.2

Valid 63 100.0 Missing 0 Total 63 Subpopulation 63a

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Table A.3. Table confusion matrix.

Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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The Validity of MLR and ANN in Predicting Sukuk Rating

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Muhammad Luqman Nurhakim, Zainul Kisman & Faizah Syihab

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The Validity of Multinomial Logistic Regression and Artificial Neural Network in Predicting Sukuk Rating: Evidence from Indonesian Stock Exchange

1. Introduction

5.5. JII X5

5.6. Predictive accuracy

6.5. Predictive accuracy